184 D.A. Seale et al. J. of Economic Behavior Org. 44 2001 177–200
4. Results
This section provides graphical displays and statistical summaries of the results of the present study as well as compares these results with those of DSR. We begin with an analysis
of the impact of information disparity on the decisions and profit of our subjects. Later in the paper we report the results of testing the learning model.
Condition SA : Fig. 2 displays the 50 asks all the individual data points plotted against
the 50 reservation values for each of the 10 sellers in condition SA. Superimposed on the scatter plot is the piecewise LES Eq. 1. On the average, the individual plots show
reasonable support for the piecewise linear prediction of the LES. Seven sellers 1, 4, 5, 7, 8, 9 and 10 followed the general pattern suggested by the LES, although many for example,
seller 7 bid more aggressively higher asks than the theory predicts. This tendency is the central focus of this paper and will be analyzed in detail below. sellers 2 and 3 exhibited
LES characteristics in their bidding but also some inclination towards fully revealing their reservation values ‘truth-telling’. Seller 6 was the only subject of all of those who have
been involved in our experiments over a 3-year period who clearly did not understand the task. In the interest of completeness his, results are included but appear spurious.
For each seller, we estimated a piecewise linear spline function to fit the data in Fig. 2. The top panel of Table 1 summarizes the results for the 10 sellers: it presents the intercept,
Table 1 Linear regression results for sellers and buyers in condition SA
Buyer Intercept
Slopes by reservation value R
2
0–50 50–150
150–200 1
104.64 0.05
0.42 1.07
0.89 2
12.83 1.53
0.59 1.11
0.88 3
83.08 0.09
0.83 0.61
0.69 4
77.38 0.45
0.69 0.66
0.86 5
83.35 0.28
0.60 0.85
0.95 6
22.00 0.31
0.61 0.39
0.49 7
119.90 0.10
0.35 0.94
0.90 8
108.49 0.00
0.53 0.88
0.92 9
91.71 0.09
0.58 1.03
0.97 10
96.96 −
0.20 0.71
0.86 0.85
Median 87.50
0.09 0.60
0.87 0.89
Seller Intercept
Slope R
2
1 8.42
0.88 0.82
2 21.61
0.80 0.60
3 34.54
0.62 0.60
4 14.10
0.82 0.94
5 −
22.07 1.00
0.93 6
0.74 0.98
0.96 7
− 0.07
0.98 0.97
8 38.97
0.62 0.83
9 −
4.18 0.94
0.95 10
− 11.00
0.77 0.49
Median 6.5
0.85 0.87
D.A. Seale et al. J. of Economic Behavior Org. 44 2001 177–200 185
Fig. 2. Bids vs. reservation values for individual sellers in condition SA.
three slopes for the ranges of reservation values 0–50, 51–150, and 151–200, and the R
2
value. Turning first to the right-hand column, the R
2
values indicate a very good fit R
2
≥ 0.85 for eight of the 10 sellers, a moderately good fit for seller 3, and a poor fit, as expected,
for seller 6.
186 D.A. Seale et al. J. of Economic Behavior Org. 44 2001 177–200
Fig. 3. Bids vs. reservation values for individual buyers in condition SA.
The LES slopes for the ranges 0–50, 51–150, and 151–200 are 0, 0.67, and 1.0, respec- tively. Except for seller 6, and the conservative asks of seller 2 in the 0–50 range, the LES
appears to be a good approximation to the observed bid functions. The medians of the three slopes below the top panel clearly show the expected trend from strategic play for low
reservation values to truth-telling for high reservation values.
Turning next to the buyers, Fig. 3 displays the 50 bids plotted against the 50 reservation values for each of the 10 buyers in condition SA. There is little evidence in these plots for
D.A. Seale et al. J. of Economic Behavior Org. 44 2001 177–200 187
full revelation of the reservation values. Four buyers 1, 2, 6, and 7 almost always placed bids very close to their reservation values. Five other buyers 3, 4, 5, 8 and 9 bid below
their reservation prices but seldom as low as the LES values. Only buyer 10 consistently bid at or below the LES level and, as we shall see below, no buyer made as much money as
she did.
The regression results for the buyers, presented in the lower panel of Table 1, tell the same story. There is as much support for the truth-telling model slope = 1, intercept = 0
as there is for the LES model slope = 0.67, intercept = 16.7. Combining the results of the sellers and the buyers, we observe a general tendency of
aggressive bidding by the sellers and conservative bidding by the buyers. The net impact of these observed tendencies on realized profits is summarized in Table 2. The left-hand
column labeled A–A shows the actual payoffs in a fictitious currency called ‘francs’ that
Table 2 Payoffs by actual and hypothetical strategies in condition SA
Trader Strategy pairs
A–A
a
LE–Le
b
TT–TT
c
LE–A
d
A–LE
e
Buyer 1 710
985 1220
779 841
Buyer 2 995
1478 1696
1246 929
Buyer 3 1112
1218 1411
1235 1074
Buyer 4 1041
1245 1561
915 1231
Buyer 5 1006
1333 1544
1045 1223
Buyer 6 977
1237 1477
1192 900
Buyer 7 725
1164 1317
966 864
Buyer 8 894
1153 1363
898 1063
Buyer 9 978
1351 1474
1046 1154
Buyer 10 1142
1356 1563
1234 1203
Mean buyers 958
1252 1462
1056 1048
Seller 1 1919
1458 1505
1202 1761
Seller 2 1453
1310 1405
927 1667
Seller 3 1403
1394 1568
1004 1701
Seller 4 1721
1405 1457
1235 1806
Seller 5 1716
1328 1396
1026 1672
Seller 6 381
1408 1500
− 99
1733 Seller 7
1571 1421
1556 567
1790 Seller 8
1477 1253
1323 977
1517 Seller 9
1855 1442
1548 1251
1821 Seller 10
1474 1245
1368 845
1583 Mean sellers
1497 1366
1462 894
1705 Overall mean
1227 1309
1462 975
1377 Percentage of deals made
55.8 51.8
75.8 38.2
63.4
a
A–A: both traders play actual decisions as in experiment.
b
LE–LE: both traders play LES strategies.
c
TT–TT: both traders play their actual reservation values.
d
LE–A: buyer bids LES and seller offers as in experiment.
e
A–LE: buyer bids as in experiment and seller offers LES.
188 D.A. Seale et al. J. of Economic Behavior Org. 44 2001 177–200
were later converted into US dollars for each trader. The percentage of rounds that resulted in trade 55.8 percent is shown at the bottom of the column. The column labeled LE–LE
shows the payoff that would have accrued given the actual reservation values received in the experiment if all the subjects had played the LES for the entire duration of the
experiment. The next column labeled TT–TT shows the payoffs that would have resulted if all the traders truthfully stated their reservation values thereby maximizing efficiency.
The column labeled LE–A shows the payoffs that would have resulted if the buyers had played their LES strategies and the seller their actual strategies. In the right-hand column
labeled A–LE the roles of buyer and seller are interchanged.
Column A–A shows that, on the average, the sellers earned 56 percent more than the buyers. In comparison, were both to play their LES, the sellers’ advantage would have
declined to only nine percent. Comparison of columns 1 and 2 shows that the main source of this difference is the poor outcomes achieved by the buyers. Sellers gained slightly more than
expected relative to the LES, but buyers gained considerably less 23 percent. Individually, these results hold for all 20 subjects with the exception of seller 6. The sealed-bid mechanism
performed rather well; deals were struck in 55.8 percent of the rounds compared to 51.8 percent associated with LES play. Table 2 further shows that despite this relatively high
percentage of trades made, more than six percent of the potential total profit achievable in the experiment under LES was left on the table.
Condition SLA : When the information disparity favoring the sellers is increased, the
results are similar to those of condition SA with the payoff disparities magnified. Fig. 4 displays the 50 asks plotted against the 50 reservation values for each seller sep-
arately. The piecewise LES functions Fig. 1 are superimposed on each scatter plot. The support for the LES prediction is as good as before. For six sellers 2, 4, 6, 7, 9, and, in
particular, 10, the correspondence is remarkable. Most sellers made more aggressive asks than the LES whereas others deviated in the direction of truth-telling sellers 3 and 8.
The bids of the 10 buyers not displayed here are similar to those reported in Fig. 3 for condition SA. Nearly all bids fall somewhere between the LES and the reservation values
showing as much support for truth-telling as for strategic play. Only buyer 6 placed her bids at or below the LES level.
As in condition SA, we have a combination of most sellers in condition SLA bidding more aggressively than the LES and nearly all buyers bidding less aggressively. Using
the same format as Tables 2 and 3 presents a summary of the payoffs that did or would have accrued to each trader. Again, we see a pronounced information effect. Column 1 of
Table 3 shows that, on the average, the sellers in condition SLA earned 96 percent more than the buyers. In comparison, with both parties playing their LES, the sellers’ advantage
would have been reduced to 41 percent. Comparison of columns 1 and 2 of Table 3 shows that, on the average, the sellers gained 11 percent more than expected relative to the LES
whereas the buyers lost 20 percent. Individually, all buyers lost relative to the LES compare columns A–A and LE–LE, and all but one of the 10 sellers gained. Table 3 further shows
that deals were struck in 75 percent of all rounds compared to the 70.6 percent predicted by the LES.
Condition BAC : When combined with the corresponding buyer advantage results of our
previous research, conditions SA and SLA suggest a strong information effect in bilateral bargaining. The next section examines the dynamics of this effect. But first we report the
D.A. Seale et al. J. of Economic Behavior Org. 44 2001 177–200 189
Fig. 4. Bids vs. reservation values for individual sellers in condition SLA.
results of condition BAC, which replicates Experiment 1 of DSR in which the buyers had the information advantage.
When provided with the same sequence of reservation values as the traders in Experiment 1 of DSR, the 10 buyers in condition BAC bid as shown in Fig. 5. These buyers were matched
with the same random sequence of sellers each of whom receiving the same sequence of
190 D.A. Seale et al. J. of Economic Behavior Org. 44 2001 177–200
Table 3 Payoffs by actual and hypothetical strategies in condition SLA
Trader Strategy pairs
A–A LE–LE
TT–TT LE–A
A–LE Buyer 1
1372 1595
2117 978
1545 Buyer 2
1469 1725
2472 1036
1606 Buyer 3
1311 1692
2154 670
1409 Buyer 4
1492 1901
2462 965
1715 Buyer 5
1451 1767
2362 992
1492 Buyer 6
1110 1842
2374 841
1489 Buyer 7
1512 1798
2189 1123
1651 Buyer 8
1294 1616
2182 906
1349 Buyer 9
1673 1898
2326 1134
1665 Buyer 10
1440 1807
2422 851
1562 Mean buyers
1412 1764
2306 950
1548 Seller 1
2452 2497
2308 989
2849 Seller 2
2982 2511
2325 265
2891 Seller 3
2702 2503
2312 1236
2890 Seller 4
2726 2471
2261 1745
2635 Seller 5
2892 2505
2312 861
2881 Seller 6
2833 2510
2312 511
2793 Seller 7
2898 2512
2329 1570
2984 Seller 8
2551 2494
2296 1894
2910 Seller 9
2899 2494
2295 1476
2938 Seller 10
2853 2497
2310 2194
2871 Mean sellers
2778 2499
2306 1274
2864 Overall mean
2095 2132
2306 1112
2206 Percentage of deals made
75.0 70.6
96.4 33.4
81.6
reservation values as in the DSR study. The only difference was that the programmed sellers unknown to the buyers always bid their LES values.
A comparison of Fig. 5 with the corresponding plots from Experiment 1 of DSR shows ad- ditional evidence of buyers bidding less aggressively. Most buyers bid at or slightly above the
LES levels buyers 1, 2, 3, 5, 6, 7 and 9. Only buyer 4 bid in an extremely aggressive fashion. Mean bids for all 10 buyers over the three ranges of reservation values defined by the breaks
in the LES function, were compared with the corresponding bids from DSR. For reservation values above 150, the LES offer for a buyer was 116.7. In condition BAC, buyers submitted
mean bids 120 above this value. In contrast, the buyers in DSR submitted mean bids consid- erably lower 111. This difference between the two studies is statistically significant F =
9.598, p 0.002, serving to indicate that the LES and more aggressive asks of the pro- grammed sellers in condition BAC elicited more conservative bidding on the part of buyers.
Of even more interest, consider the profits obtained in condition BAC Table 4. Even though the information advantage is with the buyers, the sellers obtain slightly higher
profits-at, or in many cases above the LES levels. For convenience, the corresponding summary results of DSR are reproduced in the bottom panel of Table 4. Note the differences:
D.A. Seale et al. J. of Economic Behavior Org. 44 2001 177–200 191
Fig. 5. Bids vs. reservation values for individual buyers in Experiment 1 of DSR.
playing against human subjects, the buyers in the DSR study profited greatly from their information advantage. In the BAC condition, the LES-programmed sellers erased all of
this advantage and more. Column 5 of Table 4 bottom panel shows the payoffs which would have occurred in the original DSR experiment if sellers had placed LES bids and
buyers had bid as they actually did in the experiment. The impact on profits is to modestly
192 D.A. Seale et al. J. of Economic Behavior Org. 44 2001 177–200
Table 4 Payoffs by actual and hypothetical strategies in condition BAC
Trader Strategy pairs
A–A LE–LE
TT–TT LE–A
A–LE Buyer 1
1483 1549
1582 1549
1483 Buyer 2
1231 1412
1546 1412
1231 Buyer 3
1099 1463
1543 1463
1099 Buyer 4
698 1491
1624 1491
698 Buyer 5
1052 1409
1569 1410
1052 Buyer 6
1392 1542
1604 1542
1392 Buyer 7
1118 1416
1543 1416
1118 Buyer 8
1148 1426
1553 1426
1148 Buyer 9
1176 1474
1535 1474
1175 Buyer 10
1223 1454
1564 1454
1223 Mean buyers
1162 1464
1566 1464
1162 Seller 1
1486 1481
1582 1481
1485 Seller 2
1147 1234
1546 1234
1146 Seller 3
1405 1319
1543 1319
1405 Seller 4
415 1389
1624 1389
415 Seller 5
1744 1309
1569 1308
1745 Seller 6
1382 1545
1604 1545
1381 Seller 7
1337 1270
1543 1270
1338 Seller 8
1000 1345
1553 1345
999 Seller 9
1550 1388
1535 1388
1551 Seller 10
982 1395
1564 1395
982 Mean sellers
1245 1368
1566 1368
1245 Overall mean
1203 1416
1566 1416
1203 Percentage of deals made
42.6 52.4
76.4 52.4
42.6 Experiment 1 of DSR
Mean buyers 1457
1439 1536
1577 1182
Mean sellers 1028
1315 1536
1125 1112
Overall mean 1242
1377 1536
1125 1147
Percentage of deals made 51.6
52.6 77.0
57.8 40.8
improve those of the sellers and greatly reduce those of the buyers. This analysis, of course, ignores any changes the buyers might make during the experiment if sellers were to bid in
this fashion. Table 4 shows that actual buyers, in the face of such aggressive bidding by the sellers, would adaptively retreat during the experiment and the sellers would do even better.
In fact, the mean asks of the nine sellers excluding seller 4 who faced the inflexible buyer 4 is nearly as high as the expected LES values. Clearly there is a lesson to be learned here;
this topic is explored further in the concluding section of the paper.
5. A reinforcement-based adaptive learning model
